关键词: zero-inflated exponential distribution, casualty rate, collision, maritime accident

Abstract: There are two weaknesses in current researches into human casualty of ship collision. One is that the range of injuries or fatalities is restricted to the maximum number of casualties in a particular sample, which may not cover all the possible numbers of casualties in the future. International Maritime Organization (IMO) employed the injured or dead percentage of all the persons on board to represent casualties, but it only provided several discrete values to quantify human losses in different scenarios. The other is that the assumption that the distributions of the injuries or fatalities follow certain distribution, such as negative binomial and Poisson distributions is left to be statistically tested. Firstly, this study considers casualty rate, including injury and fatality rates, as random variables; the interval of the variables are from 0 to 1. Then, the distributions of the variables are investigated using historical data. From historical data, we can find that there are many zeros. Zeroinflated models are proved to be effective in processing data with inflated zeros. Furthermore, the probability density of the variables decreases rapidly as the casualty rate becomes larger. Thus, zero-inflated exponential distribution is assumed to fit the data. The parameters of zero-inflated exponential distribution are calibrated by maximum likelihood estimation (MLE) method. Finally, the assumption is tested by chi-square test. The zeroinflated exponential distribution can be used to generate human losses as a part of consequences in the simulation of ship collision risk.

Key words: zero-inflated exponential distribution, casualty rate, collision, maritime accident